发表机构
Chalmers University of Technology; Université de Genève; SISSA; INFN, Sezione di Trieste（查尔姆斯理工大学; 日内瓦大学; 的里雅斯特国际高等研究学校; 意大利国家核物理研究所的里雅斯特分部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文用原始S矩阵自举研究四维中两种不同标量粒子的散射振幅，发现不等质量时因伪物理割线导致部分可观测量无界或单侧有界，等质量或补充信息后恢复双侧界，为π-K等过程提供起点。
AI 中文摘要
我们利用原始S矩阵自举方法，在$d = 4$维时空维度中首次研究涉及两种不同标量粒子的二到二散射振幅。我们施加一个$\mathbb{Z}_2 \times \mathbb{Z}_2$全局对称性，在该对称性下，这两个粒子是携带电荷$(-,+)$和$(+,-)$的最轻粒子，从而保证它们的绝对稳定性以及不存在三角反常阈值。对于不等质量情况，存在一个其不连续性不受物理幺正性直接约束的伪物理割线，这从性质上改变了自举问题。我们发现若干可观测量是无界的，而其他可观测量则满足非平凡的单侧界，或者一旦固定另一个可观测量就变得有界。在等质量极限下，伪物理区域消失，双侧界得以恢复。作为概念验证，我们表明通过Omnès参数化提供关于伪物理不连续性的信息也能恢复有界性。我们的结果为未来研究诸如π-K和π-核子散射等物理过程提供了起点。
英文摘要
We initiate the study of two-to-two scattering amplitudes involving two distinct scalar particles in $d = 4$ spacetime dimensions using the primal S-matrix bootstrap. We impose a $\mathbb{Z}_2 \times \mathbb{Z}_2$ global symmetry under which the two particles are the lightest ones carrying charges $(-,+)$ and $(+,-)$, guaranteeing their absolute stability and absence of triangular anomalous thresholds. For unequal masses, the presence of a pseudo-physical cut whose discontinuity is not directly constrained by physical unitarity qualitatively changes the bootstrap problem. We find several observables to be unbounded, while others obey non-trivial one-sided bounds or become bounded once another observable is fixed. In the equal-mass limit, where the pseudo-physical region disappears, two-sided bounds are recovered. As a proof of concept, we show that supplying information about the pseudo-physical discontinuity through an Omnès parametrisation also restores boundedness. Our results provide a starting point for future studies of physical processes such as pion-kaon and pion-nucleon scattering.
Comments34 pages + appendices, 22 figures
